Theory of Impact

Abstract

So far we have considered problems concerning the statics and dynamics of discrete (lumped) and continuous material systems when forces of action and reaction act upon these systems in a continuous fashion for the entire duration of a process. On the other hand, it is known that changes in system momentum leading to changes in velocity are associated with the action of a force or moment of force during a finite and often very short time interval. A phenomenon is called an impact if we observe a sudden (instantaneous) change in the velocity of a particle caused by the action of instantaneous forces. Despite the passage of several years, the notions of instantaneous changes in velocities and forces of an infinitely short duration time are intuitive, and to date they have not found an adequate mathematical description. If two bodies collide and the time of the collision process is very short, then we observe a continuous change in the velocity of the body, and because the collision usually lasts for a very short time, it is associated with the generation of relatively large forces. However, it should be emphasized that the notions of “small” and “large” quantities are relative and subjective.